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Ch.9- t- statistic, Alternatives to Pearson r, Ch.14- Correlation and…

- - - - Null hypothesis means value of mean has not changed
    - - .
  - - - Step 3-
        Calculate test statistic
        (1st find sample variance s^2 = SS / df;
        2nd find standard error sM = √(s2 / n);
        3rd find t statistic t = M - µ / sM)
        
        Step 4-
        Make a decision regarding H0
- - - - Calculate the deviation/difference from the mean and the sum of squared deviations
        
        M - µ; then subtract that number from each score in the distribution
        
        Then compute the sum of squared deviations (SS) from the new scores
        
        subtract new SS from total SS
        
        Put that number as numerator of fraction with total variance as denominator. Turn into percent
        
        This percent is r^2
        
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  - - - It is the interval of values around the sample mean that we can be reasonably confident the population mean falls in
        
        Using df to estimate or find t score
        
        Then, use formula
        µ = M + and - tsM
        
        this is the formula for the confidence interval and will break up the graph into body and tail(s)
        
        The width of the confidence interval changes with the confidence level selected (80%, 90%, 99%)
        
        To gain confidence, increase your interval width
        
        Sample size changes it too. The bigger the sample, the more precise (smaller) the interval because the sM decreases
- - - - instead of n, n - 1 is used
      - .
- - - - How well a t distribution approximates a normal distribution is determined by df
        
        Larger the df, the closer to a normal distribution
    - - Anything that effects sM will effect rejection of H0
        
        Sample size
        
        Larger the sample means smaller the error means more likely to have an effect
        
        Sample variance
        
        larger variance means larger error means less likely to have an effect
- - - - compute with ranks, not original scores
  - - - rs = 1 - 6∑D^2 / n(n^2 - 1)
- - - - dichotomous variable is assigned a number first
        
        then solve for r
- - - - Then find pearson
        
        (chi-square statistic is more common
- - - - Direction
        
        The sign (+ or-) of the relationship
        
        Positive: go in the same direction
        
        ex. Y increases as X increases
        
        Negative: go in opposite directions
        
        Ex. Y decreases as X increases
      - Form
        
        Linear
        
        When points on scatter plot cluster around a straight line
      - Strength
        
        The consistency and predictability of a relationship
        
        Ex. if X increases by 1 point, Y will increase by a predictable amount
        
        Perfect Correlation: 1.00 or -1.00: Perfectly consistent
        
        0 describes no consistency
  - - - r = SP / √(SSxSSy)
        
        Find the means for Xs and Ys
        
        Find deviations by subtracting M from value
        
        Square the deviations
        
        Add together = SSx and SSy
        
        Multiple SSx by SSy
        
        1 more item...
        
        Multiple the X deviation by the Y deviation for each pair
        
        Add together = SP
        
        Divide SP by the square root of the product of SSx and SSy = r
        
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    - - r = the degree to which X and Y vary together / the degree to which X and Y vary separately
        
        or, covariability of X and Y / variability of X and Y separately
      - r^2 is more accurate. IT is called the coefficient of determination
        
        Ex. a correlation of r = +.60, using r^2, shows that 36% of Y is explained by X
    - - Measures covariability: SP = ∑(X - Mx)(Y - My)
        
        Find the X deviation and Y deviation for each individual
        
        Find the product of the deviations for each individual
        
        Add the products
        
        SP = ∑XY - ∑X∑Y / n
        (n is pairs of scores)
        
        Same
        
        .
    - - Z score would then be two scores, zx and zy
        
        for sample: r = ∑zxzy / (n-1)
        
        For population: p = ∑zxzy / N
- - - - total squared error = ∑(Y - Yhat)^2
        
        least squared error = Yhat = bX + a
  - - - a = point where line intercepts y-intercept
        a = My - bMx
        
        Standardize line with z scores
        
        zhat = (beta)zx
        
        zy = rzx
  - - - = √(SSresidual / df)
  - - - MSregression = SSregressions / dfregression
        
        F = MSregression / MSresidual
- - - - Is H0 from sampling error, or is there a real nonzero correlation?
- - - - t = r - p / (√1-r^2 / n-2)